Related papers: Killing Vector Fields of Standard Static Space-tim…
The conditions for the existence of Killing-Yano tensors, which are closely related to the appearance of non-generic world-line SUSY, are presented for static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set of…
We explore spacetime torsion in a two-dimensional setting, wherein it corresponds to a vector field. Without invoking field equations of a particular gravitational theory, we develop visualization techniques for such torsion fields,…
We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies under physically relevant regularity…
It is proven that a solution to the Einstein-Maxwell equations whose gravitational and electromagnetic radiation fields vanish is in fact stationary in a neighbourhood of spatial infinity. That is, if the Weyl and Faraday tensors decay…
Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\delta K^\flat =0$ by using the Killing non-linear 1-form $K^\flat$ and the spray operator $\delta$ with the Finsler non-linear…
We present a classification of hamiltonian vector fields on multisymplectic and polysymplectic fiber bundles closely analogous to the one known for the corresponding dual jet bundles that appear in the multisymplectic and polysymplectic…
We provide a general method for studying manifestly $O(n+1)$ covariant formulation of $p$-form gauge theories by stereographically projecting these theories, defined in flat Euclidean space, onto the surface of a hypersphere. The gauge…
The most general form of non-static plane symmetric space-times is considered to study proper curvature collineations by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in…
We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is…
A new curvature obstruction to the existence of a timelike (resp. causal) Killing or homothetic vector field $X$ on an even-dimensional (odd-dimensional) Lorentzian manifold, in terms of its timelike (resp. null) sectional curvature is…
On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source,…
The Einstein Equation on 4-dimensional Lorentzian manifolds admitting recurrent null vector fields is discussed. Several examples of a special form are constructed. The holonomy algebras, Petrov types and the Lie algebras of Killing vector…
We show how one can systematically construct vacuum solutions to Einstein field equations with $D-2$ commuting Killing vectors in $D>4$ dimensions. The construction uses Einstein-scalar field seed solutions in 4 dimensions and is performed…
States of a generic quantum field theory on a curved spacetime are considered which satisfy the KMS condition with respect to an evolution associated with a complete (Killing) vector field. It is shown that at any point where the vector…
We present a clear and practical way to characterize the parabolicity of a complete immersed surface that is invariant with respect to a Killing vector field of the ambient space.
A vector field $V$ on any (semi-)Riemannian manifold is said to be mixed Killing if for some nonzero smooth function $f$, it satisfies $L_VL_Vg=fL_Vg$, where $L_V$ is the Lie derivative along $V$. This class of vector fields, as a…
This paper investigates axially symmetric space-times that admit a homothetic vector field based on Lyra's geometry. The cases when the displacement vector is a function of $t$ and when it is constant are studied. In the context of this…
It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike…
Integrable Killing tensors are used to classify orthogonal coordinates in which the classical Hamilton-Jacobi equation can be solved by a separation of variables. We completely solve the Nijenhuis integrability conditions for Killing…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…